Theoretical Analysis of Non Linear Behavior of Rubber Bush for Optimum Shape Form

Theoretical Analysis of Non Linear Behavior of Rubber Bush for Optimum Shape Form Shrikant G. Ingle PG Student, S.S.G.B.C.O.E.&T Department of Mechanical Engineering, Bhusawal-425203, North Maharashtra University, Maharashtra, India. R. B. Barjibhe Faculty of S.S.G.B.C.O.E. & T Department of Mechanical Engineering, Bhusawal-425203, North Maharashtra University, Maharashtra, India. Abstract- In modern day s customer s requirement of comfort is increasing day by day. This paper is related to damping of vibration caused by engine by designing a rubber bush. For an internal combustion engine, there exist two basic dynamic disturbances: the firing pulse due to the explosion of the fuel in the cylinder; the inertia force and torque caused by the rotating and reciprocating parts (piston, connecting rod and crank). To damp out such forced vibration engine is supported by rubber bush. In this study theoretical analysis is done with using suitable formulae to investigate the static deflection, behavior of rubber bush with focusing on the effect of material compressibility on numerical results. Keywords Rubber Bush, Axial Stiffness, Lateral Stiffness. I. INTRODUCTION Nowadays, people require high quality for everything. Certainly the comfort in the moving vehicles is peoples concern so it is desirable to have high performance suspension systems for vehicles. Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road. Vibration is undesirable, wasting energy and creating unwanted sound, noise. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations can be caused by imbalances in the rotating [1] parts, uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted vibrations. Forced vibration is when a time-varying disturbance (load, displacement or velocity) is applied to a mechanical system. The disturbance can be a periodic, steady-state input, a transient input, or a random input. The periodic input can be a harmonic or a non-harmonic disturbance. Examples of these types of vibration include a shaking washing machine due to an imbalance, transportation vibration (caused by truck engine, springs, road, etc. Natural rubber consists of suitable polymers of the organic compound isoprene, with minor impurities of other organic compounds plus water. Forms of polyisoprene that are useful as natural rubbers are classified as elastomers. Rubber is a unique material that is both elastic and viscous. Rubber parts can therefore function as shock and vibration isolators and/or as dampers. Although the term rubber is used rather loosely, it usually refers to the compounded and vulcanized material. Rubber like material exhibit a highly nonlinear behavior characterized by hyper elastic deformability and incompressibility. It is a material which can withstand very large strain from 100% to 1000% without any permanent deformation. Theoretical formulation is carried out in this seminar work and CAD model is prepared as per the dimensional requirement. The axial and lateral loads are considered to calculate the [13] stiffness. Future work contains FEA analysis and Experimental validation with theoretical analysis. II. PROBLEM DEFINITION The main purpose of rubber bush in automobile is to support the engine firmly and to eliminate the noise & vibration. The rubber bushes supporting the engine are subjected to forced vibrations caused by moving parts of engine and unbalanced forces. This unbalanced forces cause s failure of rubber bush. The main aim is to increase the life cycle of the rubber bush for engines and to determine the optimum shape form of the rubber bush reducing manual iteration for those by using ABAQUS Software. By using this FEA tool Optimum shape form of rubber bush can be achieved. Vol. 3 Issue 3 January 2014 212 ISSN: 2278-621X

III. RUBBER Natural rubber consists of suitable polymers of the organic compound isoprene, with minor impurities of other organic compounds plus water. Forms of polyisoprene that are useful as natural rubbers are classified as elastomers. Currently, rubber is harvested mainly in the form of the latex from certain trees. The latex then is refined into rubber ready for commercial processing. Natural rubber is used extensively in many applications and products, either alone or in combination with other materials. In most of its useful forms, it has a large stretch ratio, high resilience, and is extremely waterproof. Rubber is a unique material that is both elastic and viscous. Rubber parts can there-fore function as shock and vibration isolators and/or as dampers. To improve the mechanical properties of rubber Natural rubber is compounded, vulcanized along with anti-degrading agents, reinforcement agents. Vulcanization forms chemical bonds between adjacent elastomeric chains and subsequently imparts dimensional stability, strength, and resilience. Rubber like material exhibit a highly nonlinear behavior characterized by hyperelastic deformability and incompressibility. It is a material which can withstand very large deformation more than 100% of its original shape. The typical stress-strain curve in tension is noticeably nonlinear so that Hook s law cannot be used and it is not possible to assign a definite value to the young s modulus except in the region of small strains. Rubber exhibit complicated mechanical behavior as it can undergo large deformations. IV. RUBBER BUSH A bushing or rubber bushing is a type of vibration isolator. It provides an interface between two parts, damping the energy transmitted through the bushing. A common application is in vehicle suspension systems, where a bushing made of rubber (or, more often, synthetic rubber or polyurethane) separates the faces of two metal objects while allowing a certain amount of movement. This movement allows the suspension parts to move freely, for example, when traveling over a large bump, while minimizing transmission of noise and small vibrations through to the chassis of the vehicle. A rubber bushing may also be described as a flexible mounting or anti-vibration mounting. A. Silent Bush: Silent bushes are used in automobile to support engine along with engine mount. These types of bushes are bonded by metal sleeve with the help of proper adhesives. Two metal sleeves are used one at inner portion and other at outer in between the both rubber is molded. B. Inner Bush These bushings often present in the form of an annular cylinder of flexible material outside and metallic tube inside. It is having metal in just inner portion. V. FORMULATION OF RUBBER BUSH Consider an annular rubber bush of axial length L 1 & L 2 which is bonded internally and externally to rigid circular cylindrical metal sleeves of radii r 1 and r 2, respectively. The outer sleeve is subjected to axial load of [2] [5] constant magnitude P a. Vol. 3 Issue 3 January 2014 213 ISSN: 2278-621X

Figure No.1 Rubber Bush Subjected to Load P Table No 1. Specifications of Rubber Bush Specification Dimensions Inner radius r1 9 mm Outer radius r2 18.8mm Length of outer sleeve L2 24mm Length of inner sleeve L1 31.8mm Height of rubber h 9.8 a A. Axial Stiffness K a The shear angle is thus A being the cylindrical surface area at distance r. For axial stress the rubber bush is considered as rubber spring. Through the action of force P a one sleeve moves in relation to the other by a distance X a. [8][12][16] B. Lateral Stiffness Kr The outer sleeve does not participate. The change of position of a point of the rubber layer under load Pr is considered as shear and tension or compression. [8][12][16] From Hooke's law (1) (2) (3) Hence, (4) Vol. 3 Issue 3 January 2014 214 ISSN: 2278-621X

V. RESULT AND DISCUSSION For Axial stiffness Table no 2. Values of K r When Outer Radius r 2 Varied Sr. No Outer radius Height of rubber Axial stiffness r 2 (mm) K a (N/mm) 1 18.6 9.6 195.1665 2 18.7 9.7 193.759 3 18.8 9.8 192.3793 4 18.9 9.9 191.0266 5 19 10 189.7001 Table no 3. Values of Kr When Outer Radius L1 Varied Sr. No Length of inner sleeve Height of rubber Axial stiffness L 1 (mm) K a (N/mm) 1 31.6 9.8 191.6728 2 31.7 9.8 192.0262 3 31.8 9.8 192.3793 4 31.9 9.8 192.7321 5 32 9.8 193.0845 Table no 4. Values of Kr When Length of Outer Sleeve L2 Varied Sr. No Length of outer sleeve Height of rubber Axial stiffness L 2 (mm) K a (N/mm) 1 22 9.8 185.5862 2 23 9.8 189.0119 3 24 9.8 192.3793 4 25 9.8 195.6918 5 26 9.8 198.9530 For Lateral stiffness Table no 5. Values of Kr When Outer Radius r2 Varied Sr. No Outer radius Height of rubber Lateral stiffness r 2 (mm) K r (N/mm) 1 18.6 9.6 324.0535 2 18.7 9.7 325.0284 3 18.8 9.8 326.0016 4 18.9 9.9 326.9734 5 19 10 327.9437 From above table by changing the parameters of rubber bush the axial stiffness comes out to be K a = 192.3793N/mm and Lateral stiffness K r = 326.0016 N/mm. The CAD Model is drawn in CATIA V5 and general views are shown in this paper further FEA analysis is to be done with the help of ABAQUS and finally will be validated by experimentation. Vol. 3 Issue 3 January 2014 215 ISSN: 2278-621X

(a) Figure No.2 (a) CAD Model of Rubber Bush showing general views (b) Front View of Rubber Bush (b) VI. CONCLUSION This paper covers introduction and properties of rubber. Natural rubber consists of suitable polymers of the organic compound isoprene, with minor impurities of other organic compounds plus water. Forms of polyisoprene that are useful as natural rubbers are classified as elastomers. Viscoelastic behavior of rubber is studied critically. The rubber bush is being used to support engine firmly and to reduce noise and vibration. Theoretical modeling of rubber bush subjected to both axial and lateral loads are considered and the static stiffness of rubber bush is calculated by using standard formulation. CAD models were prepared by using dimensions as per customer requirement by using CATIA V5. REFERENCES [1] Umesh S. Ghorpade, D. S. Chavan, Vinaay Patil & Mahendra Gaikwad, Finite Element Analysis and Natural Frequency Optimization of Engine Bracket. IJMIE ISSN No. 2231 6477, Vol-2, Iss-3, 2012. [2] C.H. Park, H.J. Shim, D.H. Choi, J.K. Kim and S.M. Lee, Shape Optimization of Rubber Isolators in Automotive Cooling Modules for the Maximization of Vibration Isolation and Fatigue Life. International Journal of Automotive Technology, Vol. 13, No. 1, Pp. 61 [3] T. Ramachandran, K. P. Padmanaban, Review on Internal Combustion Engine Vibrations and Mountings, IJESET, August 2012 Volume 3, Issue 1, pp: 63-73. [4] Martin Ostberg, LeifKari, Transverse, Tilting and Cross-Coupling Stiffness of Cylindrical Rubber Isolators in the Audible Frequency Range. The Wave-Guide Solution Journal of Sound and Vibration 330 (2011) 3222 3244. [5] G.E. Tupholme, An Analogy between Radially-Loaded Rubber Bush Mountings and Axially-Loaded Bonded Rubber Blocks, Materials and Design 32 (2011) 5038 5042. Vol. 3 Issue 3 January 2014 216 ISSN: 2278-621X

[6] Qian Li, Jian-cai Zhao, Bo Zhao, Fatigue Life Prediction of a Rubber Mount Based on Test of Material Properties and Finite Element Analysis, Engineering Failure Analysis 16 (2009) 2304 2310. [7] R.A. Ibrahim, Recent advances in nonlinear passive vibration isolators, Journal of Sound and Vibration 314 (2008) 371 452. [8] J.M. Horton, G.E. Tupholme. Approximate radial stiffness of rubber bush mountings. Materials and Design 27 (2006) 226 229. [9] A. Dall Asta, L. Ragni, Experimental Tests and Analytical Model of High Damping Rubber Dissipating Devices. Engineering Structures 28 (2006) 1874 1884. [10] Young Kong Ahn, Jin Dae Song, Bo-Suk Yang, Optimal Design of Engine Mount Using an Artificial Life Algorithm. Journal of Sound and Vibration 261 (2003) 309 328. [11] A.F.M.S. Amin, M.S. Alam, Y. Okui. An Improved Hyperelasticity Relation in Modeling Viscoelasticity Response of Natural and High Damping Rubbers in Compression: Experiments, Parameter Identification and Numerical Verification. Mechanics of Materials 34 (2002) 75 95. [12] J. S. Tao, G. R. Liu and K. Y. Lam, Excitation Force Identification of an Engine with Velocity Data at Mounting Points. Journal of Sound and Vibration (2001) 242(2), 321-331. [13] ] Seong Beom Lee, Alan Wineman. A Model for Non-Linear Viscoelastic Coupled Mode Response of an Elastomeric Bushing. International Journal of Non-Linear Mechanics 35 (2000) 177-199. [14] J. S. Tao, G. R. Liu and K. Y. Lam, Design Optimization of Marine Engine Mount System. Journal of Sound and vibration (2000) 235(3), 477-494. [15] M.V. Blundell, The Influence of Rubber Bush Compliance on Vehicle Suspension Movement. Materials and Design 19 (1998) 29-37. [16] E. F. Gobel, Rubber Springs Design. John Wiley and Sons, 1974 New York, pp 20-40. Vol. 3 Issue 3 January 2014 217 ISSN: 2278-621X